I very much doubt there is any closed-form formula for the antiderivative, so you probably need to contemplate numerical integration for the general case of ##\int_a^b f(x) \, dx##. However, before doing that, sit down and think carefully about your specific problem.

I have already told you it cannot be done with formulas---even very long ones having billions of complicated terms and taking millions of pages to write out. However, that was not your original question: you wanted ##\int_{-3}^3 f(x) \, dx##. As I suggested, think hard about the problem first.

In order to use symmetry here you must also show that this is not an improper integral. Your integrand is a fraction with sin(x^4+ 5x^2+ 100) in the denominator. Can you show that this never 0 for x between -3 and 3?

In order to use symmetry here you must also show that this is not an improper integral. Your integrand is a fraction with sin(x^4+ 5x^2+ 100) in the denominator. Can you show that this never 0 for x between -3 and 3?

There is an x in the denominator instead of sine. Moreover, the function doesn't seem to defined within the given limits.